(CNN) -- Five Iranians held in Iraq by the United States since 2007 went back to Tehran on Sunday, Iran's government-backed Press TV reported.

They were greeted at the airport by dozens of cheering men, who placed wreaths around their necks and carried them on their shoulders from the plane to the airport building, Press TV pictures showed. Some in the crowd flashed victory signs, while others took pictures of the returning men.

Three of the men, who were released by the United States on Thursday, said they were diplomats. They were detained in Irbil, a city in Iraq's Kurdish region, on January 11, 2007.

It is not clear who the other two men are.

However, Iranian Foreign Ministry spokesman Hassan Qashqavi said their release will not directly affect chilly relations between Iran and the United States, according to the semi-official Fars News Agency.

"Freedom of these people is not directly related to the issue of Iran and the U.S. and the two countries' diplomatic relations," Qashqavi said on the sidelines of a ceremony welcoming the men home, Fars reported.

The U.S. military said the men seized in Irbil had been thought to be connected to Iran's Islamic Revolutionary Guard Corps Quds Force, a group believed to be providing funds, weapons, roadside bomb technology and insurgent training. Two were freed in November 2007.

The U.S. military said they had been thought to be connected to Iran's Islamic Revolutionary Guard Corps Quds Force, a group believed to be providing funds, weapons, roadside bomb technology and insurgent training.

There has been action recently on a number of long-running detentions in Iraq.

The bodies of two British hostages kidnapped two years ago in Baghdad were recently returned to Britain. The condition of three other men seized at the same time was not known.

Last month, the Iraqi government freed a man who had been held in the killing of five U.S. soldiers, a government spokesman said Tuesday.

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Laith al-Khazali was detained in March 2007 along with his brother Qais in the killing of the soldiers in the central city of Karbala two months earlier.

There had been media reports that al-Khazali would be among a number of militiamen -- all with links to Iran -- who would be released in exchange for the freeing of five Britons kidnapped two years ago from the Iraqi Finance Ministry in Baghdad.

Al-Khazali's release was a gesture by the Iraqi government as part of the national reconciliation process with militant groups, said Ali al-Dabbagh, the Iraqi government spokesman.

However, he said that the release was not linked to any rumored negotiations about the British hostages or to any other deal.